Debt Instruments and Markets Professor Carpenter

Floating Rate Notes

Concepts and Buzzwords

. Floating Rate Notes – floater, FRN, ARN, – Cash flows VRN, benchmark – Valuation interest rate, index – Interest Rate Sensitivity

Reading . Veronesi, Chapter 1 . Tuckman, Chapter 18

Floating Rate Notes 1 Debt Instruments and Markets Professor Carpenter

Introduction to Floating-Rate Notes . A floating rate note is a with a that is indexed to a benchmark interest rate. . Possible benchmark rates include US Treasury rates, , prime rate, municipal and mortgage interest rate indexes. . Examples of floating-rate notes – Corporate (especially financial institutions) – Adjustable-rate mortgages (ARMs) – Governments (inflation-indexed notes)

Floating Rate Jargon

. Other terms used for floating-rate notes include . FRNs . Floaters and Inverse Floaters . Variable-rate notes (VRNs) . Adjustable-rate notes . FRN usually refers to an instrument whose coupon is based on a term rate (3-month T-bill, 6- month LIBOR) . VRNs are based on longer-term rates . (1-year T-bill, 5-year T-bond)

Floating Rate Notes 2 Debt Instruments and Markets Professor Carpenter

Cash Flow Rule for Plain Vanilla Semi- Annual Floater

. The basic semi-annual coupon floating rate note has the coupon indexed to the 6-month interest rate. . Each coupon date, the coupon is equal to the of the note times one-half the 6-month rate quoted 6 months earlier, at the beginning of the coupon period. In other words, the time t coupon

payment as percent of par is t-0.5rt . . The note pays par value at .

Floating Rate Note Cash Flows

. Each coupon is based on the previous 0.5-year rate. . Only the next coupon is known at the current date. The later ones are random.

0 0.5 1 ... t ... T

Floating Rate Notes 3 Debt Instruments and Markets Professor Carpenter

Example: Two-Year Semi-Annual Floater What are the cash flows from $100 par of the note in this scenario? . The first coupon on the bond is 100 x 0.0554/2=2.77. . Later coupons set by the future 6-month interest rates. . For example, suppose the future 6-month interest rates turn out as follows: 0 0.5 1 1.5 2 5.54% 6.00% 5.44% 6.18% Floater Cash Flows: 0 0.5 1 1.5 2 2.77 3.00 2.72 103.09

100 x 0.06/2

Replicating a T-Year Floater with 0.5-Year Par Bonds Consider the following trading strategy: . At time 0, buy a 0.5-year par bond: pay $1. . At time 0.5, buy another 0.5-year par bond:

collect $1+ r0.5/2, pay $1 = collect $r0.5/2 . At time 1, buy another 0.5-year par bond:

collect $1+0.5r1/2, pay $1 = collect $0.5r1/2) . and so on, every six months until floater maturity date T

. At time T: collect $1+T-0.5rT/2

Floating Rate Notes 4 Debt Instruments and Markets Professor Carpenter

0 0.5 1 1.5 ... T

A Semi-Annual-Coupon Floater is Equivalent to a 0.5-Year Par Bond . A dynamic strategy of strategy of rolling six-month par bonds until floater maturity, collecting the coupons along the way, replicates the cash flows of a floater. . So as semi-annual coupon floater is equivalent to the six- month par bond in its replicating trading strategy. . Like its replicating trading strategy, a floater is always worth par on the next coupon date with certainty. . Its coupon is set to make it worth par today. . The duration of the floater is therefore equal to the duration of a six-month par bond. . Their convexities are the same too.

Floating Rate Notes 5 Debt Instruments and Markets Professor Carpenter

Class Problems Assume the 0.5-year rate is 5.54%.

1) What is the duration of a semi-annual paying floating-rate note?

2) What is the dollar duration of $100 par of this note?

3) What is the convexity of this floater?

4) What is the dollar convexity?

Floating Rate Notes 6